1. Field of the Invention
Embodiments of the invention relate generally to a Post-Viterbi error correction method and apparatus. More particularly, embodiments of the invention relate to a Post-Viterbi error correction method and apparatus adapted to reduce a probability of faulty error correction.
2. Description of Related Art
Error detection and correction techniques play an important role in many data transmission systems where noise is present and accuracy matters. For example, in many electronic data transmission systems, error detection and correction is achieved by encoding data using some form of redundant data before transmitting the data across a channel and then using the redundant data to aid a process of decoding the data.
One common technique used for error correction is known as a cyclic redundancy check (CRC). In a cyclic redundancy check, data to be transmitted across a noisy channel is multiplied by a generator polynomial to form a codeword.
In this written description, the term “transmitted codeword” will denote an original codeword to be transmitted across a channel and the term “detected codeword” will denote the codeword as detected by a receiving device after the codeword has been transmitted across the channel. In addition, the generator polynomial can be referred to more generically as an error detection code, which can be designed from various types of polynomials.
A syndrome is computed from the detected codeword by dividing the detected codeword by the generator polynomial. A detected codeword without errors yields an all-zero syndrome, and a detected codeword containing errors yields a syndrome that is not all-zero.
A post-Viterbi processor is often used to find a most probable type of error event (error type) and a start position for the error event within a detected codeword by estimating an amount of correlation between known forms of error events and an estimated error signal.
The estimated error signal is typically computed as a difference between an output signal of an equalizer and a signal generated by convolution of an output of a Viterbi decoder with a partial response polynomial. The partial response polynomial is a signal that facilitates a digitalization of an analog readback channel by reshaping the analog readback channel into a known partial response using an equalizer. The Viterbi decoder computes the detected codeword from a reshaped, digitalized equalizer output.
Due to noise and an imperfect equalizer, the detected codeword may contain errors. Accordingly, the error signal is obtained by subtracting the equalizer output from the signal computed by convolving the Viterbi decoder output with the partial response polynomial.
As an example, FIG. 1 shows one type of post-Viterbi processor. Referring FIG. 1, data is encoded by an error detection coding (EDC) encoder (not shown) and transmitted through a channel which may contain noise. An equalizer unit 106 reshapes a readback channel output into a sequence which is matched to a partial response P(D), where “D” is a delay variable in a digital sequence, e.g., P(D)=1+6D+7D2+2D3.
A partial response maximum likelihood (PRML) unit 108 detects a transmitted codeword and provides an output. An error signal ‘e’ is generated by subtracting an output of equalizer unit 106 and the output of PRML unit 108, convolved with partial response P(D).
An EDC decoder unit 112 computes a syndrome to check for the presence of errors in the detected codeword. A matched-filters unit 114 comprises a plurality of error-event matched filters, each corresponding to a dominant error event and used to detect whether the detected codeword contains one of the dominant error events. Each error-event matched filter calculates a likelihood value, or a confidence value, that an error event occurred in the detected codeword. A select maximum unit 116 then estimates a type and position of a most likely error event. Then, based on the information about the type and position, a correction unit 118 corrects the error event.
As an example of how the post-Viterbi processor works, assume that “a” is recorded data, “a prime” (a′) is recorded data decoded by PRML 108 and P(D) is a partial response polynomial. An output signal “y” of equalizer unit 106 and an error signal “e” can be expressed as y=a*p+n and e=(a−a′)*p+n, respectively, where “p” denotes a transfer function of a readback channel between the medium where the recorded data is stored and the output of the equalizer, “n” denotes noise in the readback channel, and * denotes a convolution operation.
A confidence value calculated by matched filters unit 114 can be expressed as an equation of P−1(D)*E−1(D), where, P−1(D) and E−1(D) denote time reversals of the partial response polynomial and an error event, respectively, and * denotes an convolution operation. Respective error event matched filters in matched filters unit 114 are used to calculate a probability of each error event, e.g., a confidence value, at every position within a detected codeword.
Select maximum unit 116 produces an error type and an error start position based on the largest confidence value among outputs of matched filters unit 114. Correction unit 118 then corrects an error event according to the error type and the error start position output from select maximum unit 116.
In channels with a relatively high incidence of errors (i.e., “interference-dominant” channels), errors tend to occur in specific patterns. For example, if a transmitted codeword is [1, −1, 1, −1, 1, 1, −1, 1, −1, −1], and a detected codeword is [1, −1, 1, −1, 1, −1, 1, −1, −1, −1], then an error event [0, 0, 0, 0, 0, 2, −2, 2, 0, 0] with a with a specific pattern denoted [2, −2, 2] has occurred.
FIG. 2 is a flow chart illustrating a conventional Post-Viterbi error correction method.
Referring to FIG. 2, an operation S202 is performed to determine whether or not an error event has occurred in a detected codeword. In operation S202, the detected codeword is divided by a generator polynomial to produce a syndrome. If the syndrome is all zero, then the detected codeword presumably contains no errors. However, if the syndrome is not all zero, the detected codeword presumably contains some error.
If the detected codeword is determined to be error free, a data recovery process is performed in an operation S206 to recover original data from which the detected codeword was formed. The data recovery process typically removes redundant bits that were added to the data by the EDC encoder to form a transmitted codeword.
On the other hand, if the detected codeword is determined to contain errors in operation S202, a Post-Viterbi error correction process is performed in an operation S204 to correct the errors.
Operation S204 is performed under a condition of K=1, where “K” denotes a maximum number of error events which are assumed to have possibly occurred within the detected codeword. The relation of K<E should be satisfied, where “E” denotes a number of error event matched filters included in the post-Viterbi processor.
In operation 204, confidence values are computed for all possible error events with respect to every bit of the detected codeword using respective error event matched filters corresponding to respective error events. Here, each error event matched filter is configured according to dominant error events occurring in the readback channel. Errors in the detected codeword are corrected according to the most likely error event that occurred and the most likely start position of the error event, as determined by the post-Viterbi processor.
Unfortunately, conventional Post-Viterbi error correction methods, such as that shown in FIG. 2, have a high possibility of mis-correction. A mis-correction occurs where either a wrong type of error is corrected, or an error event is corrected at the wrong start position.
For example, in perpendicular magnetic recoding (PMR), an error event ±[2,−2] is often detected as ±[2,−2,2] or [2,−2,0,2,−2]. Another dominant error event [2,−2,2] is often detected as [2,−2] or [2,−2,2,−2,2,−2]. Similarly, error events ±[2,−2,2,−2,2] and [2,−2,2,−2,2,−2] are also commonly mis-detected. On the other hand, with regard to mis-corrected start positions, dominant error events [2,−2] and ±[2,−2,2] are often corrected as [2,0,−2] or [2,0,0,−2].
FIG. 3 shows an example of a mis-correction by a Post-Viterbi processor. In particular, FIG. 3 shows result of an error correction with a condition where an actual error event is [2,−2] and an actual error position is [137, 138]. In other words, in the example, error event [2, −2] occurred at positions of [137, 138], where dominant error events used in a Post-Viterbi processor are [2,−2], [2,−2,2], [2,−2,2,−2], [2,−2,0,2,−2], [2,−2,2,−2,2] and [2,−2.2,−2,2,−2].
As seen in FIG. 3, the error event with the largest confidence value is [2,−2] and the corresponding error positions are [83, 84]. Accordingly, error correction is performed on bits 83 and 84 within the codeword.
However, because the actual error position is [137, 138] such an error correction, as shown in FIG. 3, becomes a mis-correction by a mis-error position designation.